Control of a train of high purity distillation columnsfor efficient production of 13C isotopes

Clara Ionescu, Roxana Both, Csaba Fustos, Clement Festila, Mihai Gligan and Robin De Keyser

Abstract—It is well-known that high-purity distillation columnsare difficult to control due to their ill-conditioned and stronglynonlinear behaviour. The fact that these processes are operatedover a wide range of feed compositions and flow rates makes thecontrol design even more challenging. This paper proposes themost suitable control strategies applicable to a series of cascadeddistillation column processes. The conditions for control andinput-output relations are discusssed in view of the global controlstrategy. The increase in complexity with increased number of se-ries cascaded distillation column processes is tackled. Uncertaintyin the model parameters is discussed with respect to the dynamicsof the global train distillation process. The main outcome of thiswork is insight into the possible control methodologies for thisparticular class of distillation processes.

Index Terms—multivariable control, uncertainty, process in-dustry, distillation column, isotopes, carbon.

I. INTRODUCTION

PROCESS control did not reach where it stands todayif it wasn’t for the continuous and strenuous efforts of

control engineers for better and more efficient methods oftackling nonlinear, time-varying, multivariable and constraintproblems [1]. The extensive literature survey from [2] ondistillation dynamics and control suggests to the reader that theprocess of distillation is the most common unit of operationin the chemical industry and it represents a teacher’s pet whenit comes to illustrate control problems for training controlengineers. Along with the numerous possibilities in tacklingcontrol issues, the process of distillation brings numerousconstraints and challenges, being in itself a complete stand-alone process within the chain of industrial applications [1].

An excellent reader’s digest on dynamics and control ofdistillation columns are [4] and [3]. Both of these vast worksare a necessary guide through the jungle of various distillationcolumn configurations and specifications for control. However,a special class of distillation processes are those aimingat stripping various chemical elements. There is a lack ofpapers in the literature discussing this particular class, despiterenewed interest from the control community [5]. Most ofthe existing works on control of distillation columns examinethe problem from an individual column standpoint. However,multi-column systems have been examined in cases where

C.M. Ionescu, R. Both, Cs.Fustos and C. Festila are with the TechnicalUniversity of Cluj Napoca, Department of Control Engineering, 28 Memo-randumului street, 400114 Cluj-Napoca, Romania.

R. De Keyser and C. M. Ionescu are with Ghent University, Departmentof Electrical energy, Systems and Automation, Technologiepark 913, B9052Gent-Zwijnaarde, Belgium. Corresponding author: Clara M. Ionescu; tel:0032-9-264-5608; fax: 0032-9-2645839.

M. Gligan is with the National Institute for Research and Development ofIsotopic and Molecular Technologies (NIRDIMT), Cluj-Napoca, Romania.

recycle streams are present between the columns creatingchain interactions, with some applications in azeotropic distil-lation systems. Multiple columns in a plantwide environmenthave been explored in a variety of case studies of multiunitprocesses with reaction and separation sections. In thesecases, multivariable model based (predictive) control is anexcellent candidate for plantwide control with ability to tackledead-times and constraints, either in global control, either indistributed control structures [6], [7].

The Carbon element has two stable isotopes: base compo-nent (12C) with the natural abundance of 98.89 at% and theheavier stable isotope (13C), with 1.11 at% concentration [9]–[11]. Using dedicated equipment, it is possible to detect if asubstance contains a larger concentration of (13C), suggestingits synthetic origin. Based on this feature, the (13C) isotopemay be used in different applications and fields like scien-tific research, bio-medicine, environmental protection, etc [8].The carbon monoxide with high-purity in (12C) is used inelectronics technology to produce synthetic diamond crystalswith 50% better thermal conductivity than that of the usualsynthetic crystals [9]. It is also very effective in detectingtumour in the human body [18] and broadly used in otherclinical investigations [17]. An effective method to producesubstances with high-concentration of these valuable isotopesis based on the cryogenic distillation of carbon-monoxide [9].

There are very few plants worldwide which can performthis complex operation. Among them is the National Institutefor Research and Development of Isotopic and MolecularTechnologies (NIRDIMT) from Cluj-Napoca, Romania [16].The current bottleneck in this problem is the low efficiencyof the high-purity stripping distillation, making the processunattractive from an economical point of view. The verycomplex stripping process requires large scale setups, withoutimplicit efficiency. A pragmatic approach to solve this issue isto use trains of striping distillation columns. However, whenclosed loop control is involved, series of distillation columnswith recycle streams can endanger the stability of the overallprocess and care must be taken when choosing the controlconfiguration. The objective of this paper is to discuss theseproblems and propose solutions for safe operation and efficient(13C) isotope production.

The structure of the paper is as follows: first, some theoreti-cal background on controlling distillation columnsis presented,followed by a numerical example of the column for strippingthe (13C) isotope.

2015 20th International Conference on Control Systems and Science

978-1-4799-1780-8/15 $31.00 © 2015 IEEE

DOI 10.1109/CSCS.2015.150

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Fig. 1. Schematic of one CO stripping distillation column with possibility toseries connect to a second column.

II. THE ISOTOPE SEPARATION COLUMN

There are several available methods able to increase theconcentration of the (13C) isotope in some substances. Oneof them is that of cryogenic distillation of carbon monoxide[9]. For pure carbon-monoxide situations, at the vaporizationtemperature of nitrogen (≈ 190oC), the liquid and gaseousphase co-exist [16]. Because the maximum vapor pressureby (12CO) is higher than the pressure of (13CO), the (13C)accumulates in the liquid phase, where it may be collectedand extracted as final product. In the static contact of bothphases, the increase in concentration is very small. As givenby the separation factor (α), here we have a value very closeto unity, i.e. α ' 1.011 [9]–[11]. A continuous counter currentof an ascendant gaseous stream and a descendent liquid streamof carbon-monoxide increases the (13C) concentration in theliquid phase and decreases it in the gas phase, which is thenevacuated as waste. One dedicated equipment can offer anenrichment in (13C) only up to 8-10 at%, due to the abovedescribed physical limitations.

The (13C) isotope separation column of the National Insti-tute for Research and Development of Isotopic and MolecularTechnologies (NIRDIMT) from Cluj-Napoca is a steel packedpipe as depicted in Fig. 1, fed with pure gaseous carbon-monoxide by the flow-rate and (13C) isotope concentrationat 1.11%at [9]. The isotope of interest (13C), accumulated inthe liquid carbon-monoxide, is withdrawn as final product atthe flow rate and concentration. The gaseous carbon monoxidewith lower (13C) concentration is evacuated as waste at thetop side, by flow rate and the concentration, which is in factthe secondary product of the separation column. The efficientthermal isolation of the column is based on the externalvacuum jacket. If cryogenic distillation temperature is used,the vapor pressure of carbon monoxide with (12C) is greaterthan the pressure of carbon monoxide with (13C), hence theisotope (13C) accumulates in the liquid phase. This processis called the rectifying process. Simultaneously, a decrease

in the concentration of (13C) in gaseous phase, is achievedduring the stripping proces. In order to rise the (13C) isotopeconcentration up to a desired level, a permanent counter-current of the liquid-gaseous phases must be ensured. This isprovided by an electrically heated boiler in the column baseand a condenser, cooled with liquid nitrogen at the columntop side. The liquid nitrogen level in the condenser and theliquid carbon-monoxide in the boiler must be maintained ata constant level for optimal operation of the column. Thegeneric task of the control system is to keep the (13C) isotopetransfer rate constant, which can be achieved by variouscontrol configurations.

III. SINGLE-COLUMN CONTROL CONFIGURATIONS

A. Classical Control Approach

Each distillation column is unique through its design andstructure and a generic rigorous modelling and control ap-proach is not a realistic objective. However, to some extent,distillation columns for separation processes have some com-mon properties, such as thermodynamic principles and basicdynamics, which will be employed hereafter to discuss theclassical control approach.

Typically, a high purity distillation column is connectedin series to another train of distillation columns [5]. Thebottom product streams of these prior columns are bufferedinto a level-controlled tank and fed into the high-purity column(HPC). Hence, the feedflow is varied stepwise instead ofcontinuous. However, the variations in the composition aresmooth. In case of a stripping process of series of HPCs, thetop product streams directly into the feedflow of the next HPC.In this case, smooth continuous variations in the feedfloware expected as well as feed compositions. The monitoredvariables are typically top pressure in the column and top levelcontrol of the cooling liquid.

The composition dynamics are most important for controlsince variations in one HPC in series will affect the input,hence the dynamics of the next HPC. The product compo-sitions are a nonlinear function of the reflux, boilup, andfeed comdition. For instance, a 5% increase of the refluxflow rate improves the top product composition with a certainamount, but the same percent decrease degrades it much more.There are also very strong interactions in the HPC; e.g. achange of reflux or boilup alters both product compositions.The interaction between both product compositions and refluxand boilup has a severe consequence for the compositiondynamics, known as ill-conditioned behaviour.

The control objectives of HPC can be summarized asthreefold:• control of the material balance• product quality control• maintaining constraintsThe first objective includes the control of the vapor holdup

(top pressure), the reflux accumulator level, and the reboilerlevel. Practically, these control objectives are easily achievedby simple PI controllers. The second objective is the mostimportant since it is related to the optimal economic andecologic operation of the DHC [21]. It is well known that

50

tight control of both product qualities minimizes the energycomsumption and delivers within-specs products. However,this is a challenging control task due to the presence ofdisturbances such as variations of the feedflow rate and feedcomposition (recall that is a series train of HPC). Tightcomposition control requires advanced control schemes andhas been the subject of several important works [2], [3], [19],[20]. Reflux, boilup and pressure drop are allowed to varywithin a predefined range. Any operation of a distillationcolumn outside this range may cause insufficient separationor even physical damage of the setup.

A typical control problem of HPC has five controlledvariables: top composition, bottom composition, reflux accu-mulator level, reboiler level and top pressure; and has fivemanipulated variables: reflux, boilup (e.g. via reboiler duty),top product flow rate, bottom product flow rate, cooling liquidflow rate. Due to the high inherent sensitivity of multivariablecontrollers to sensor or actuator failure, the inventory control(product quality) and the composition control are indepen-dently designed, increasing robustness of the overall process.

In a first step, the two manipulated variables are selectedfor the composition control. In the specialized terminology,the choice of these manipulated variables names the controlconfiguration. An excellent overview of the various possibleconfigurations is given in [19], [20]. For instance, if the topcomposition is controlled by reflux (L) and bottom composi-tion is controlled by boilup (V), the control scheme is denotedas LV. The remaining manipulated variables are thus availablefor level and pressure control.

If a model of the HPC exists, typically in the form of alinearized model around the optimal operating point, then thechoice of the input-output variables can be done on methodsas the relative gain array, Niederlinski index or singularvalue decomposition [4], [24]. In practice, the application ofthese methods may lead to considerably different solutionsand dynamic effects due to the interaction of inventory andcomposition control are neglected.

The most common control configuration in the chemicalindustry is the LV configuration [20]. This control structure israther independent of the inventory control dynamics and hasbeen proven to have good experiemtnal results. In general,tight inventory control can be achieved with three simplePI controllers. Some distillation columns show an inverseresponse of the reboiler level to an increase of boilup. Inthis case, tight control with boilup as manipulated variablebecomes challenging and the re-selection of the manipulatedvariable may be necessary. Inverse dynamics occur in thepresence of a RHP transmission zero in the linearized modelanalysis; by changing the variable selection, such RHP zeromay be avoided.

B. Classical Modelling Approach

Robust controllers are based on the existence of a (linear)process model [13]. The development of a good model is there-fore crucial for the control system synthesis. These modelsshould describe the dynamic behaviour of the process withina wide frequency range and they can be twofold:

• system identification models• linearized models from nonlinear modelObviously, system identification around the optimal (calcu-

lated) operating point is the most pragmatic approach, but itposes some difficulties:• if time constants are large (depending on the construction

design of the HPC) , then the input-output records canbe quite time-consuming;

• since the HPC has a high sensitivity to changes inthe internal flow rates, it is difficult to define ’small’amplitude variations in the input which will not exceedthe linear region;

• each identification experiment will cause disturbances inthe product quality

• such models are valid only around the operating pointwhere they were identified.

These dis-advantages make system identification not aninteresting approach; instead, linearization of nonlinear mod-els is preferred and modelling uncertainty is allowed to betackled by the choice of the control structure. The problemsarising from the linearization process are related to idealizingassumptions, such as:• constant pressure drop• constant and equal enthalpies on all trays• constant total holdup on all trays (equimolar flow)

which of course, are not realistic. The first assumption means aneglect of the correlation between tray pressures, holdups, andboilup rates. The second assumption implies uniform vaporflows within the stripping section and within the rectifyingsection of the HPC. The assumption of a constant tray holdupneglects in part flow dynamics. These assumptions introducein the model high frequency errors, which may be critical ifa fast performance given by a large bandwidth of the closedloop is envisaged.

C. Modelling Uncertainty

Model uncertainty and lack of validity in the operating rangecan seriously affect the overall plant stability and robustness[14], [15]. Typical sources of model uncertainty for HPCare measurement errors, limited actuator speed, unmodelledhigh frequency dynamics, process nonlinearity. In the caseof HPC, which are highly nonlinear plants, the error of alinear model rapidly increases with the distance from theoperating point where it was identified/linearized. Additionalstochastic disturbances will also affect the process dynamics,in which case the error cannot be determined. This errorbetween the process model and the process itself can bemodelled either as a single frequency-dependent uncertaintybound (i.e. unstructured uncertainty), or as several frequency-dependent uncertainy bounds (i.e. structured uncertainties).

Several types of uncertainty bounds can be implemented,tackling various practical aspects. Of these, we mention:• input uncertainty• model uncertainty• measurement uncertainty

and we discuss the essential solutions for each of themhereafter.

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Fig. 2. Multiplicative uncertainty for the HPC input.

The actual values of the manipulated variables reflux andboilup will never match exactly the values requested by thecontrol system. Moreover, this error will also be frequencydependent, because: i) static and dynamic measurement errorsof reflux and reboiler duty; ii) actuator resolution; iii) changingheat of evaporation due to pressure and temperature variations;iv) reboiler and actuator lags; v) effects of sampling (i.e. digitalsystems).

The bounds for relative errors in the column inputs u can bemodelled by a multiplicative uncertainty description with thefrequency-dependent error bound wuL

for the reflux L and theerror bound wuV

for the boilup V. These bounds are combinedin the matrix Wu as in figure 2.

The input uncertainty model is given by:

u(jω) = {I + ∆u(jω)Wu(jω)}u(jω) (1)

with||∆u(jω)||∞ ≤ 1 (2)

and

Wu(jω) =

[wuL

(jω) 00 wuV

(jω)

](3)

It has been shown in [22] that the performance of the closedloop for a HPC is very sensitive to errors in the manipulatedvariables. For controller design (and analysis) the error boundsWu need to be estimated as good as possible, especially inthe low frequency range where the condition number of thecolumn model is high. The risk is lower control performanceif overestimation occurs. In this low frequency range, theerrors of the manipulated variables at the plant input arestrongly dominated by flow measurement errors and parametervariations. For instance, if boilup is controlled indirectly by thesteam flow rate, a change in the heat of evaporation will causeerrors in vapor flow rate leaving the reboiler. Calibration ofthe flow meters is therefore crucial.

The effects of reboiler lags, actuator lags, dynamic mea-surement errors and sampling period are present in the highfrequency range. These errors increase with the frequency andcan easily exceed 100% of the nominal values for frequenciesabove 1 rad/min. In this case, the steady-state error togetherwith the high-frequency error can be approximated by a firstorder lead/lag transfer function:

G(s) = K1 + s/ωN

1 + s/ωD(4)

with ωN , ωD, the gain K represents the steady state error andcut-off frequencies chosen for ωD > 10ωN .

The model uncertainty has twofold origins: i) column non-linearity and ii) un-modelled dynamics. The highly nonlinearbehaviour of HPC is observed at varying operating points andat transients during disturbance rejection. This depends on thevarying internal flow rates (L and V) and on the compositionprofile within the distillation column, represented by the liquidand vapor phase compositions.

Any type of control system for HPC will exhibit large gainsin the low frequency range to achieve small control errors atsteady-state. Transients have no significant effect in the lowfrequency range and the internal vapor and liquid flow ratesas well as the composition profile within a column becomea function of feed flow rate and composition only. However,the dynamic behaviour of a HPC depends substantially on thetrue composition profile and the true internal vapor and liquidflow rates. Consequently, the operating range of a HPC canbe bounded with a maximum and a minimum feed flow rateand composition. In this framework, it follows that the largestinternal flow rates will exist for the smallest feed compositionand largest feed flow rate. Similar reasoning indicates thatthe smallest internal flow rates will exist for the largest feedcomposition and smallest feed flow rates. hence, the lowfrequency behaviour of a HPC is bounded by the models formaximum and minimum column load.

The simplest way to represent the column nonlinearity dueto varying operating points would be to use a multiplicativeoutput uncertainty. Assuming the uncertainty for each modeloutput independent of the actual value of the other modeloutputs, one has:

y(jω) = {I + ∆y(jω)Wy(jω)}y(jω) (5)

with

||∆y(jω)||∞ ≤ 1 (6)

and

y(jω) = GN (jω)

[d(jω)u(jω)

](7)

with GN the transfer function matrix of the plant at nominaloperating point and Wy a diagonal matrix similar to (3).Care must be taken with such uncertainty representation sincethe low frequency range tends to have a high multiplicativegain, which is prohibited for any control design. However,things become simpler if the errors are highly correlated, i.e.the variation of the steady-state operating points causes asimultaneous increase/decrease of the singular values of thetransfer functions from the control signals u to the modeloutputs y. This statement can be evaluated by means ofNyquist plots for individual channels ui → yi. Notice thatthe effect of transients obeys the laws of a rather unstructureduncertainty. Due to the nonlinear vapor/liquid equilibrium, thesingular values of the transfer functions Gu→yj may changein different directions, which pose other control challenges.

The second origin for model uncertainty was un-modelleddynamics. Most of the works in literature treat the effect offlow dynamics in an input time delay τ , with 0 < τ < 1minute [23].

52

Finally, measurement uncertainty can be well exemplifiedby temperature measurements. These can be well approx-imated by a first order lag modelling the behaviour of atemperature sensor. The time constant of this model dependson the position of the temperature sensor. If the sensor isplaced in the liquid phase, time constant of the order of 1minute can be expected. However, if the sensor is placed inthe vapor phase, it can go up to 10 minutes or more. Thegain of the model is related to sensor calibration and heat lossto the environment. For the case of our HPC, heat losses areclose to zero (vacuum jacket) and calibration is assumed to becorrect.

The complete uncertainty model consists of input uncer-tainty (1), model uncertainty (5) and performance specifica-tions. Simple dynamic models are used whenever possible,to avoid further uncertainy blocks. The advantage of suchmodelling approach is that the entire operating range of theHPC is covered.

D. Improved Control Approach

From an economic point of view, disregarding the controland measurement problems, two-point control is obviously thebest, i.e. both composition loops closed. This follows since theoptimal operating point corresponds to some given purity spec-ification. In case of stripping HPCs, these are not independent.There is also a case when one-point control is optimal, i.e.when the column is operated at maximum capacity. In the LVconfiguration, by controlling one composition, inherently wecontrol the other (i.e. strongly coupled). If one can measure thefeed rate, and implement a feedforward controller by using theratio L/F, then we achieve self-regulation of F. In this way, oneachieves acceptable control of both products (top and bottom)if single end control of bottom composition is used and fixedL/F ratio.

Feed composition sensitivity analysis is used to determineof a single-end control structure would be effective. Thisis achieved with dedicated software, based on steady-statesimulations. Typically, one checks the percent variation of therequired reflux flow rate and reflux ratio over the range of feedcompositions. Depending on the estimated values, it may beindicated that for HPC a single end control structure with afixed reflux-to-feed ratio would outperform a fixed reflux ratiostructure [5]. The basic control structure is depicted in figure3 and suggested improved structure in figure 4 as following.In a train of series HPC, the feed comes in on flow/levelcontrol from the upstream column. Pressure is controlledby manipulating condenser duty. Reflux can be ratioed tofeed, and reflux-drum level is controlled by manipulating theflow rate of the distilate product. Base level is controlled bymanipulating the flow rate of the bottoms. Temperature is notcontrolled directly, but from the pressure measurements at topand bottom HPC trays, its reference value can be estimatedand controlled by reboiler duty.

Competing rules for distillation control need to be nego-ciated. For instance, analysis suggests that the reflux-drumlevel is controlled by reflux because of very high reflux ratio.However, it also suggests that the reflux should be ratioed

Fig. 3. Schematic of a basic control structure of one HPC within a train ofseries HPCs.

Fig. 4. Proposed control structure of one HPC within a train of series HPCs.

to the feed. Obviously, these are not independent, hencecannot be achieved simultaneously. An ingenious solutionis given in [5], summarized as follows and illustrated infigure 5. This control structure is similar to the previous one

53

Fig. 5. Another proposed control structure of one HPC within a train of seriesHPCs.

proposed, except the following: reflux-drum level is controlledby manipulating reboiler duty and the distillate impurity iscontrolled by manipulating the control valve in the distillateline.

The control structure from figure 5 is unusual because ofthe use of reboiler heat input to control the reflux-drum level.This is based on the assumption that the feed compositionsensitivity analysis requires very small changes in the ratio,hence it can be fixed. The liquid level in the reflux drum canbe controlled by distillate - this will fail if the flow rate is muchsmaller than the reflux. In the latter case, the reboiler duty canbe employed efficiently to solve this dilemma, if the changesin vapor flow rates in the column are fast. The distillatecomposition is controlled by the distillate flow rate. Usinghigh gain control, it is possible to achieve faster response ofvapor boilup to level changes. These are then detected by thelevel controller, which changes the vapor rate up the columnand affects distillate composition. Notice that the pressurecontroller manipulating condenser duty is nested inside thecomposition control loop.

Two-point control will not be adressed here, but we maysuggest some ideas. The liquid flow dynamics decouple thetwo column ends (top and bottom) at high frequency. If effortis put into making the quality loops fast enough, good controlcan be achieved for both compositions. This can be doneusing temperature measurements, or in our case inference frompressure measurements, with an outer composition cascadeloop. In other words, a combination of the control schemessuggested in figure 4 and figure 5.

IV. NUMERICAL EXAMPLE

A. Single column

For the column from Fig 1, the transfer function matrix isgiven by: −0.111

s2+1.094s+0.08420.1152

s2+1.211s+0.2021 0−0.0017

s2+0.1343s+0.00190.0038

s2+0.1547s+0.0043−1.104

s+0.1176−0.0099

s2+1.056s+0.07030.0062

s2+1.085s+0.09858.457

s+0.9851

(8)

where the time delay has been ignored for simplicity andwith inputs and outputs verified by the relative gain arrayas following: i) first manipulated input is the output wasteflow from the column to control the pressure in the columnat the condenser zone, ii) the second manipulated input is thefeed flow to the column to control the liquid carbon monoxidelevel in the boiler, and iii) the third manipulated input is theelectrical power supplied to the boiler resistor, to control thepressure in the column at the boiler zone. The dependenceof the relative gain array with frequency depicted in Fig 6suggests that for step changes in the controlled variables, thepairing is optimal.

Fig. 6. Dependance of frequency of the relative gain array for one column.

Further analysis into the magnitudes of the transfer functionmatrix from (8) suggests that the bandwidth of the system isaround 0.1 rad/s, as in Fig 7.

Finally, the singular value decomposition suggests that thefirst pair of input-output variables may pose most difficulty forcontrol if the bandwidth of the system is increased to obtainbetter perfromance in terms of smaller settling times. Fig. 8depicts these values as a function of frequency.

B. The train of distillation columns

The real life setup deals with a cascade of three columns[16]. The permanent counter-current of liquid and gaseousphase is ensured by a common condenser cooled with liquidnitrogen and by three different boilers, one for each column,heated with electrical resistors. Studying the coupling pos-sibilities of the three columns, the conclusion was to feed

54

Fig. 7. Gains of the system for one column.

Fig. 8. Singular values of the system for one column.

the first column with carbon monoxide, the enriched gaseousphase from the first column being used as feed for the secondcolumn and the product of the second column as feed for thethird column, ensuring maximum enrichment in (13C) withminimum equipments. Previous studies revealed that the majorinfluence on the end product in a separation column has thevapor upstream, which is maintained by the electrical resistorof the boiler. This was the reason why the authors have chosento implement in present work the distributed control of theresistor powers for the cascade of three columns.

For the second column from Fig 9, the transfer functionmatrix is given by:

−0.111s2+1.111s+0.1011

0.1152s2+1.311s+0.3033 0

−0.0017s2+0.1300s+0.0022

0.0038s2+0.1500s+0.0044

−1.104s+0.1200

−0.0099s2+1.060s+0.0784

0.0062s2+1.105s+0.1225

8.457s+0.9800

(9)

Fig. 9. Schematic of the stripping train of distillation columns.

and for the third column is given by: −0.111s2+1.131s+0.1213

0.1152s2+1.361s+0.3538 0

−0.0017s2+0.145s+0.003

0.0038s2+0.1700s+0.0060

−1.104s+0.1400

−0.0099s2+1.085s+0.0985

0.0062s2+1.120s+0.133

8.457s+0.9850

(10)

The interaction matrices for the reflux from the second columnto the first and from the third column to the second are givenby 0 0 0

110s+1

110s+1 0

0 0 0

(11)

and 0 0 01

7.5s+11

7.5s+11

7.5s+1

0 0 0

(12)

, respectively.From a practical standpoint, all loops within a HPC can

be taken as P-controlled (proportional gain only). In this way,fast dynamics can be achieved. However, since compositionfeedback control usually has slow dynamics, a PI-control canbe used as an outer loop. This results in a cascaded controlscheme, which seem to be the optimal solution from the aforementioned analysis. The controller parameters are given by:

C11(s) = −0.4923s+ 0.03678

s(13)

C22(s) =1.937s+ 0.03622

s(14)

C33(s) =0.16s+ 0.16

s(15)

C44(s) = −0.3881s+ 0.04709

s(16)

C55(s) =1.835s+ 0.04126

s(17)

C66(s) =0.17s+ 0.17

s(18)

C77(s) = −0.3156s+ 0.05707

s(19)

C88(s) =1.899s+ 0.07255

s(20)

55

C99(s) =0.18s+ 0.18

s(21)

Analysis of the sensitivity functions reveal in Fig. 10 that themost difficult to control is the first column, since all dynamicspropagate from it into the output of the last column, as perglobal control objective.

Fig. 10. Schematic of the stripping train of distillation columns.

The most economic control scheme will only use onedistillate composition sensor at the output of the third HPC. Inthis case, there are several possibilities for global control. Firstpossibility is to use cascade control with composition of thethird column output as the outer loop and temperature (viapressure) control in the same column. The first and secondHPC are not controlled for composition output, only keptwithin a desired (i.e. calculated) range for level, feed flowrate and pressure values. This is a relatively simple solution,if tight control is not necessary. Second possibility is to usetight control in each HPC, and global control for composition,measured at the output of the third column. This implies ahyerarchical or distributed control strategy, where each columnis controlled separately for its optimal operation, but sincethey interact with each other, a global cost index (typicallyrelated to the composition) provides the operating conditionsand reference values for each of them. This is a more complexproblem in terms of stability, but still numerically acceptablefor real-life implementation. Third possibility is to view theensemble of the series train of HPCs as a input-output block,with intermediate variables, in a centralized control strategy.Intuitively, inputs will be those entering the first column andoutputs will be those from the third column. The drawbacksof this scheme are the model complexity and the intrinsiccoupling effects between columns due to recirculation, asdepicted in figure 9. The latter can be avoided by very goodcondenser and reboiler operation, i.e. avoiding high variationsin the pressures at the column ends.

V. CONCLUSION

This paper presented some first ideas on the control of atrain of high purity concentration distillation columns. The

study case was developed around the stripping process of the(13C) isotope, a valuable product in a manifold of applications.As the control methodology is further developed, insight intothe problem will become available to further improve thiscomplex process.

ACKNOWLEDGMENT

This work was supported by a grant of the RomanianNational Authority for Scientific Research, CNDI UEFISCDI,project number 155/2012 PN-II-PT-PCCA-2011-3.2-0591.

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